Results 51 to 60 of about 145,855 (140)
Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco +3 more
wiley +1 more source
Journal of Function Spaces, 2017 We study a singular Schrödinger-Kirchhoff-Poisson system by the variational methods and the Nehari manifold and we prove the existence, uniqueness, and multiplicity of positive solutions of the problem under different conditions.
Mengjun Mu, Huiqin Lu
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Journal of Function Spaces, 2020 In this paper, the nonlinear quasilinear elliptic problem with the logarithmic nonlinearity −div∇up−2∇u=axφpulogu+hxψpu in Ω⊂Rn was studied. By means of a double perturbation argument and Nehari manifold, the authors obtain the existence results.
Zhoujin Cui +4 more
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Planar Choquard equations with critical exponential reaction and Neumann boundary condition
Mathematische Nachrichten, Volume 297, Issue 10, Page 3847-3869, October 2024.Abstract We study the existence of positive weak solutions for the following problem: −Δu+α(x)u=∫ΩF(y,u)|x−y|μ1dyf(x,u)inΩ,∂u∂η+βu=∫∂ΩG(y,u)|x−y|μ2dνg(x,u)on∂Ω,$$\begin{equation*} \begin{aligned} \hspace*{65pt}-\Delta u + \alpha (x) u &= {\left(\int \limits _{\Omega }\frac{F(y,u)}{|x-y|^{{\mu _1}}}\;dy\right)}f(x,u) \;\;\text{in} \; \Omega,\\ \hspace ...
Sushmita Rawat +2 more
wiley +1 more source
Journal of Function Spaces, 2019 This paper deals with the Kirchhoff-Schrödinger-Poisson system involving sign-changing weight functions. We prove the existence and multiplicity of solutions to the system. Our main results are based on the method of Nehari manifold.
Dandan Yang, Chuanzhi Bai
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Non‐autonomous double phase eigenvalue problems with indefinite weight and lack of compactness
Bulletin of the London Mathematical Society, Volume 56, Issue 2, Page 734-755, February 2024.Abstract In this paper, we consider eigenvalues to the following double phase problem with unbalanced growth and indefinite weight, −Δpau−Δqu=λm(x)|u|q−2uinRN,$$\begin{equation*} \hspace*{3pc}-\Delta _p^a u-\Delta _q u =\lambda m(x)|u|^{q-2}u \quad \mbox{in} \,\, \mathbb {R}^N, \end{equation*}$$where N⩾2$N \geqslant 2$, 1
Tianxiang Gou, Vicenţiu D. Rădulescu
wiley +1 more source
, 2018 This paper is concerned with variational continuation of branches of solutions for nonlinear boundary value problems, which involve the p p -Laplacian, an indefinite nonlinearity, and depend on a real parameter λ \lambda
Kaye Silva, Yavdat Ilyasov
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Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter [PDF]
, 2023 In this work we study the following nonlocal problem \begin{equation*} \left\{ \begin{aligned} M(\|u\|^2_X)(-\Delta)^s u&= \lambda {f(x)}|u|^{\gamma-2}u+{g(x)}|u|^{p-2}u &&\mbox{in}\ \ \Omega, u&=0 &&\mbox{on}\ \ \mathbb R^N\setminus \Omega, \
Tripathi, V. M., Mishra, P. K.
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Ground states for Schrodinger-Poisson systems with three growth terms
Electronic Journal of Differential Equations, 2014 In this article we study the existence and nonexistence of ground states of the Schrodinger-Poisson system $$\displaylines{ -\Delta u+V(x)u+K(x)\phi u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr -\Delta\phi=K(x)u^2, \quad x\in \mathbb{R}^3, }$$ where V ...
Hui Zhang, Fubao Zhang, Junxiang Xu
doaj
Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent
Journal of Inequalities and Applications, 2017 In this article, we study the existence and multiplicity of positive solutions for the quasi-linear elliptic problems involving critical Sobolev exponent and a Hardy term.
Yanbin Sang, Siman Guo
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